Given a set of vectors $S=\{\vectorlist{u}{p}\}$, their span, $\spn{S}$, is the set of all possible linear combinations of $\vectorlist{u}{p}$. Symbolically, \begin{align*} \spn{S}&=\setparts{\lincombo{\alpha}{u}{p}}{\alpha_i\in\complex{\null},\,1\leq i\leq p}\\ &=\setparts{\sum_{i=1}^{p}\alpha_i\vect{u}_i}{\alpha_i\in\complex{\null},\,1\leq i\leq p} \end{align*}